Recently there has been increased interest in signed optimal transport, which applies techniques from optimal transport to signed measures.
Signed optimal transport in one dimension has already proven itself useful in estimating parameters for seismic imaging, [1]}, [2]}, [3]}, where multiple techniques were used to change the signed signal into a positive probability measure.
Those techniques included splitting into components, exponentiating, and adding a large constant.
However, such approaches for signed optimal transport have been application specific and consequently ad hoc and a more general theory for signed measures has yet to be established.
